GKZ-systems of Feynman integrals with codimension\(=0,\;1\) 
are presented in Refs. [1]}, [2]}
through Lee-Pomeransky parametric representations [3]}.
To obtain hypergeometric series solutions with suitable independent variables,
one should compute the restricted \(D\) -module of GKZ-system originating from
Lee-Pomeransky representations on corresponding hyperplane in the parameter
space [4]}, [5]}, [6]}.
GKZ-systems of some Feynman diagrams
can be derived from their Mellin-Barnes representations [7]}, [8]}, [9]} through Miller's
transformation [10]}, [11]}.
Ref. [12]} explores the idea of bootstrap Feynman integrals using integrability,
the authors of Ref. [13]} apply GKZ description of periods to solve the
\(l\) -loop banana amplitudes with their general mass dependence, and completely clarify
the analytic structure of all banana amplitudes with arbitrary masses [14]}.
The updated summary on some classical and modern aspects of hypergeometric
differential equations is given in literature [15]}.
A Mathematica package for integrating families of Feynman integrals
order by order in the dimensional regulator from their GKZ-systems
is also given in literature [16]}.
A specialized integration algorithm for parametric Feynman integrals
with tame kinematics is also presented in literature [17]}.
Actually Cohen-Macaulay Property of Feynman Integral indicates
that the process of finding a series representation of these
integrals is fully algorithmic [18]}, and regular
singularities of Feynman Integral are determined by its Landau Discriminant [19]}.
Ref. [20]} introduces a class of polytopes to analyze
the structure of UV and IR divergences of general Feynman integrals in Schwinger parameter space.
Furthermore, Ref. [21]} elaborates on the connection among GKZ-systems, de
Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman Integrals,
and Ref. [22]} presents a Mathematica package to find linear transformations
for some classes of multivariable hypergeometric functions. In literature [23]}
the class of \(N\)  loop massive scalar self-energy diagrams with \(N+1\)  propagators
is studied, and the new convergent series representations for the 2-loop sunset diagram
with three different propagator masses and external momentum are obtained in
Ref. [24]}. The relationship between Feynman diagrams and hypergeometric functions
is reviewed in the Ref. [25]}. Using the GKZ system and its relation
to D-module theory, Ref. [26]} proposes a novel method for obtaining differential
equations for master integrals. Adopting some assumption on the virtual masses, Ref. [27]}
investigates the analytical expression of a 3-loop vacuum integral.
A new methodology to perform the expansion of multi-variable hypergeometric
functions around the time-space dimension \(D=4\)  in Ref. [28]}.
Using an algorithm that extends the Griffiths-Dwork reduction for the case
of projective hypersurfaces with singularities, the authors of Ref.[29]}
derive Fuchsian linear differential equations with respect to kinematic parameters
for a large class of massive multi-loop Feynman integrals.
